TY - JOUR
T1 - Dimensionality reduction of SDPs through sketching
AU - Bluhm, Andreas
AU - Stilck França, Daniel
PY - 2019/2/15
Y1 - 2019/2/15
N2 - We show how to sketch semidefinite programs (SDPs) using positive maps in order to reduce their dimension. More precisely, we use Johnson–Lindenstrauss transforms to pro- duce a smaller SDP whose solution preserves feasibility or approximates the value of the original problem with high probability. These techniques allow to improve both complexity and storage space requirements. They apply to problems in which the Schatten 1-norm of the matrices specifying the SDP and also of a solution to the problem is constant in the problem size. Furthermore, we provide some results which clarify the limitations of positive, linear sketches in this setting.
AB - We show how to sketch semidefinite programs (SDPs) using positive maps in order to reduce their dimension. More precisely, we use Johnson–Lindenstrauss transforms to pro- duce a smaller SDP whose solution preserves feasibility or approximates the value of the original problem with high probability. These techniques allow to improve both complexity and storage space requirements. They apply to problems in which the Schatten 1-norm of the matrices specifying the SDP and also of a solution to the problem is constant in the problem size. Furthermore, we provide some results which clarify the limitations of positive, linear sketches in this setting.
KW - Dimensionality reduction
KW - Johnson–Lindenstrauss transforms
KW - Semidefinite programming
KW - Sketching
UR - http://www.mendeley.com/research/dimensionality-reduction-sdps-through-sketching
U2 - 10.1016/j.laa.2018.11.012
DO - 10.1016/j.laa.2018.11.012
M3 - Journal article
SN - 0024-3795
VL - 563
SP - 461
EP - 475
JO - Linear Algebra and Its Applications
JF - Linear Algebra and Its Applications
ER -